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We introduce a method for obtaining the X-ray luminosity function (XLF) andthe binary-period distribution of populations of high-mass X-ray binaries(HMXBs) in the stellar fields (i.e. outside globular clusters) of normalgalaxies. We start from standard distributions of the parameters of thoseprimordial binaries which are the progenitors of HMXBs, and follow thetransformation of these ditributions with the aid of a Jacobian formalism asthe former evolve into the latter through the processes of the first masstransfer and the supernova (SN) that follows. We discuss the distributions ofthe post-SN binaries and the HMXBs. We show that our calculated model XLF has adifferential slope $\approx -1.6$ with a flattening at low luminosities, inexcellent agreement with observations. The calculated binary-perioddistribution, which basically has a slightly sloping plateau-like character atintermediate periods, with a rise to this plateau at shorter periods andfall-off from it at longer periods, is in agreement with the observeddistribution within observational uncertainties. We discuss the physical originof these distributions. We demonstrate that, while the effects of both (a) thedistribution of the properties of the massive companion in the HMXBs, and (b)the primordial orbital distribution and the SN dynamics are important, theformer appear to be dominant in determining the XLF, and the latter indetermining the HMXB binary-period distribution. We discuss the possible rolesof stellar-mass black holes and ultra-luminous X-ray sources (ULX) in theobserved "universal" XLF of HMXBs.

Collective Properties of X-ray Binary Populations of Galaxies. I. Luminosity and Orbital Period Distributions of High-Mass X-ray Binaries